Cumulative Problems - Chemistry | University of Missouri



Chapter 1: Matter, Measurement, and Problem SolvingExplain this statement in your own words and give an example.?The properties of the substances around us depend on the atoms and molecules that compose them.Explain the main goal of chemistry.Describe the scientific approach to knowledge. How does it differ from other approaches?Explain the differences between a hypothesis, a law, and a theory.What observations did Antoine Lavoisier make? What law did he formulate?What theory did John Dalton formulate?What is wrong with the expression “That is just a theory,” if by?theory?the speaker is referring to a scientific theory?What are two different ways to classify matter?How do solids, liquids, and gases differ?What is the difference between a crystalline solid and an amorphous solid?Explain the difference between a pure substance and a mixture.Explain the difference between an element and a compound.Explain the difference between a homogeneous and a heterogeneous mixture.What kind of mixtures can be separated by filtration?Explain how distillation is used to separate mixtures.What is the difference between a physical property and a chemical property?What is the difference between a physical change and a chemical change? List some examples of each.Explain the significance of the law of conservation of energy.What kind of energy is chemical energy? In what way is an elevated weight similar to a tank of gasoline?What are the standard SI base units of length, mass, time, and temperature?What are the three common temperature scales? Does the size of a degree differ among them?What are prefix multipliers? List some examples.What is a derived unit? List an example.Explain the difference between density and mass.Explain the difference between?intensive?and?extensive?properties.What is the meaning of the number of digits reported in a measured quantity?When multiplying or dividing measured quantities, what determines the number of significant figures in the result?When adding or subtracting measured quantities, what determines the number of significant figures in the result?What are the rules for rounding off the results of calculations?Explain the difference between precision and accuracy.Explain the difference between random error and systematic error.What is dimensional analysis?33.Classify each statement as an observation, a law, or a theory.All matter is made of tiny, indestructible particles called atoms.When iron rusts in a closed container, the mass of the container and its contents does not change.In chemical reactions, matter is neither created nor destroyed.When a match burns, heat is released.34.Classify each statement as an observation, a law, or a theory.Chlorine is a highly reactive gas.If elements are listed in order of increasing mass of their atoms, their chemical reactivities follow a repeating pattern.Neon is an inert (or nonreactive) gas.The reactivity of elements depends on the arrangement of their electrons.35. A chemist decomposes several samples of carbon monoxide into carbon and oxygen and weighs the resultant elements. The results are shown in the table.Do you notice a pattern in these results?Next, the chemist decomposes several samples of hydrogen peroxide into hydrogen and oxygen. The results are shown in the table.Do you notice a similarity between these results and those for carbon monoxide in part a?Can you formulate a law from your observations in a and b?Can you formulate a hypothesis that might explain your law in c?36.When astronomers observe distant galaxies, they can tell that most of them are moving away from one another. In addition, the more distant the galaxies, the more rapidly they are likely to be moving away from each other. Can you devise a hypothesis to explain these observations?The Classification and Properties of Matter37.Classify each substance as a pure substance or a mixture. If it is a pure substance, classify it as an element or a compound. If it is a mixture, classify it as homogeneous or heterogeneous.sweatcarbon dioxidealuminumvegetable soup38.Classify each substance as a pure substance or a mixture. If it is a pure substance, classify it as an element or a compound. If it is a mixture, classify it as homogeneous or heterogeneous.winebeef stewironcarbon plete the table.plete the table.41.Determine whether each molecular diagram represents a pure substance or a mixture. If it represents a pure substance, classify the substance as an element or a compound. If it represents a mixture, classify the mixture as homogeneous or heterogeneous.42.Determine whether each molecular diagram represents a pure substance or a mixture. If it represents a pure substance, classify the substance as an element or a compound. If it represents a mixture, classify the mixture as homogeneous or heterogeneous.43.Classify each of the listed properties of isopropyl alcohol (also known as rubbing alcohol) as physical or chemical.colorlessflammableliquid at room temperaturedensity?=?0.79???g?/?mLmixes with water44.Classify each of the listed properties of ozone (a pollutant in the lower atmosphere but part of a protective shield against UV light in the upper atmosphere) as physical or chemical.bluish colorpungent odorvery reactivedecomposes on exposure to ultraviolet lightgas at room temperature45.Classify each property as physical or chemical.the tendency of ethyl alcohol to burnthe shine on silverthe odor of paint thinnerthe flammability of propane gas46.Classify each property as physical or chemical.the boiling point of ethyl alcoholthe temperature at which dry ice evaporatesthe tendency of iron to rustthe color of gold47.Classify each change as physical or chemical.Natural gas burns in a stove.The liquid propane in a gas grill evaporates because the valve was left open.The liquid propane in a gas grill burns in a flame.A bicycle frame rusts on repeated exposure to air and water.48.Classify each change as physical or chemical.Sugar burns when heated in a skillet.Sugar dissolves in water.A platinum ring becomes dull because of continued abrasion.A silver surface becomes tarnished after exposure to air for a long period of time.49.Based on the molecular diagram, classify each change as physical or chemical.50.Based on the molecular diagram, classify each change as physical or chemical.Units in Measurement51.Convert each temperature.32 °F to °C (temperature at which water freezes)77 K to °F (temperature of liquid nitrogen)–109 °F to °C (temperature of dry ice)98.6 °F to K (body temperature)52.Convert each temperature.212 °F to °C (temperature of boiling water at sea level)22 °C to K (approximate room temperature)0.00 K to °F (coldest temperature possible, also known as absolute zero)2.735 K to °C (average temperature of the universe as measured from background black body radiation)53.The coldest temperature ever measured in the United States is –80 °F, recorded on January 23, 1971, in Prospect Creek, Alaska. Convert that temperature to °C and K. (Assume that –80 °F is precise to two significant figures.)54.The warmest temperature ever measured in the United States is 134 °F, recorded on July 10, 1913, in Death Valley, California. Convert that temperature to °C and K.55.Use the prefix multipliers to express each measurement without exponents.1.2?×?10???9???m22?×?10???15??s1.5?×?10?9??g3.5?×?10?6??L56.Use prefix multipliers to express each measurement without exponents.38.8?×?10?5??g55.2?×?10???10??s23.4?×?10?11??m87.9?×?10???7??L57.Use scientific notation to express each quantity with only base units (no prefix multipliers).4.5 ns18 fs128 pm35 μm58.Use scientific notation to express each quantity with only base units (no prefix multipliers).35 μL225 Mm133 Tg1.5 plete the table.plete the table.61.Express the quantity 254,998 m in each unit.kmMmmmcm62.Express the quantity?556.2?×?10???12??s?in each unit.msnspsfs63.How many 1-cm squares would it take to construct a square that is 1 m on each side?64.How many 1-cm cubes would it take to construct a cube that is 4 cm on edge?Density65.A new penny has a mass of 2.49 g and a volume of?0.349??cm?3?. Is the penny made of pure copper? Explain your answer.66.A titanium bicycle frame displaces 0.314 L of water and has a mass of 1.41 kg. What is the density of the titanium in?g?/?cm?3??67.Glycerol is a syrupy liquid often used in cosmetics and soaps. A 3.25 L sample of pure glycerol has a mass of?4.10?×?10?3??g?. What is the density of glycerol in?g?/?cm?3??68.A supposedly gold nugget displaces 19.3 mL of water and has a mass of 371 g. Could the nugget be made of gold?69.Ethylene glycol (antifreeze) has a density of?1.11??g/cm?3?.What is the mass in g of 417 mL of ethylene glycol?What is the volume in L of 4.1 kg of ethylene glycol?70.Acetone (nail polish remover) has a density of?0.7857??g/cm?3?.What is the mass in g of 28.56 mL of acetone?What is the volume in mL of 6.54 g of acetone?71.A small airplane takes on 245 L of fuel. If the density of the fuel is 0.821 g/mL, what mass of fuel has the airplane taken on?72.Human fat has a density of?0.918???g?/?cm?3?. How much volume?(?in?cm?3?)?is gained by a person who gains 10.0 lb of pure fat?The Reliability of a Measurement and Significant Figures73.Read each measurement to the correct number of significant figures. Laboratory glassware should always be read from the bottom of the meniscus.74.Read each measurement to the correct number of significant figures. Laboratory glassware should always be read from the bottom of the meniscus. Digital balances normally display mass to the correct number of significant figures for that particular balance.75.For each number, underline the zeroes that are significant and draw an?x?through the zeroes that are not.1,050,501 km0.0020 m0.000000000000002 s0.001090 cm76.For each number, underline the zeroes that are significant and draw an?x?through the zeroes that are not.180,701 mi0.001040 m0.005710 km90,201 m77.How many significant figures are in each number?0.000312 m312,000 s3.12?×?10?5??km13,127 s200078.How many significant figures are in each number?0.1111 s0.007 m108,700 km1.563300?×?10?11??m30,80079.Which numbers are exact (and therefore have an unlimited number of significant figures)?π?=?3.1412??in?=?1??ftEPA gas mileage rating of 26 miles per gallon1??gross?=?14480.Indicate the number of significant figures in each number. If the number is an exact number, indicate an unlimited number of significant figures.318,857,056 (2014 U.S. population)2.54??cm?=?1??in11.4??g?/?cm?3?(density of lead)12?=?1??dozen81.Round each number to four significant figures.156.852156.842156.849156.89982.Round each number to three significant figures.79,845.821.548937?×?10?72.34999999950.000045389Significant Figures in Calculations83.Calculate to the correct number of significant figures.9.15?÷?4.9701.54?×?0.03060?×?0.6927.5?×?1.82?÷?100.04(?2.290?×?10?6?)?÷?(?6.7?×?10?4?)84.Calculate to the correct number of significant figures.89.3?×?77.0?×?0.08(?5.01?×?10?5?)?÷?(?7.8?×?10?2?)4.005?×?74?×?0.007453?÷?2.03185.Calculate to the correct number of significant figures.43.7???2.34117.6?+?2.838?+?2.3?+?110.7719.6?+?58.33???4.9745.99???5.57286.Calculate to the correct number of significant figures.0.004?+?0.098791239.3?+?9.73?+?3.422.4???1.777532?+?7.3???48.52387.Calculate to the correct number of significant figures.(?24.6681?×?2.38?)?+?332.58(?85.3???21.489?)?÷?0.0059(?512?÷?986.7?)?+?5.44[?(?28.7?×?10?5?)?÷?48.533?]?+?144.9988.Calculate to the correct number of significant figures.[?(?1.7?×?10?6?)?÷?(?2.63?×?10?5?)?]?+?7.33(?568.99??????232.1?)???÷??5.3(?9443?+?45???–???9.9?)?×?8.1?×?10?6(?3.14???×??2.4367?)??????2.3489.A flask containing 11.7 mL of a liquid weighs 132.8 g with the liquid in the flask and 124.1 g when empty. Calculate the density of the liquid in g/mL to the correct number of significant digits.90.A flask containing 9.55 mL of a liquid weighs 157.2 g with the liquid in the flask and 148.4 g when empty. Calculate the density of the liquid in g/mL to the correct number of significant digits.Unit Conversions91.Perform each unit conversion.27.8??L?to?cm?31898 mg to kg198 km to cm92.Perform each unit conversion.28.9 nm to μm1432??cm?3??to?L1211 Tm to Gm93.Perform each unit conversion.154 cm to in3.14 kg to g3.5 L to qt109 mm to in94.Perform each unit conversion.1.4 in to mm116 ft to cm1845 kg to lb815 yd to km95.A runner wants to run 10.0 km. Her running pace is 7.5 mi per hour. How many minutes must she run?96.A cyclist rides at an average speed of 18 mi per hour. If she wants to bike 212 km, how long (in hours) must she ride?97.A certain European automobile has a gas mileage of 17 km/L. What is the gas mileage in miles per gallon?98.A gas can holds 5.0 gal of gasoline. Express this quantity in?cm?3?.99.A house has an area of?195??m?2?. What is its area in each unit?km?2dm?2cm?2100.A bedroom has a volume of?115??m?3?. What is its volume in each unit?km?3dm?3cm?3101.The average U.S. farm occupies 435 acres. How many square miles is this??(?1??acre?=?43,?560??ft?2?,?1??mile?=?5280?ft?)102.Total U.S. farmland occupies 954 million acres. How many square miles is this??(?1??acre=?43?,?560??ft?2?,?1??mi?=?5280?ft?)?. Total U.S. land area is 3.537 million square miles. What percentage of U.S. land is farmland?103.An acetaminophen suspension for infants contains 80 mg/0.80 mL suspension. The recommended dose is 15 mg/kg body weight. How many mL of this suspension should be given to an infant weighing 14 lb? (Assume two significant figures.)104.An ibuprofen suspension for infants contains 100 mg/5.0 mL suspension. The recommended dose is 10 mg/kg body weight. How many mL of this suspension should be given to an infant weighing 18 lb? (Assume two significant figures.)Cumulative Problems105.There are exactly 60 seconds in a minute, exactly 60 minutes in an hour, exactly 24 hours in a mean solar day, and 365.24 solar days in a solar year. How many seconds are in a solar year? Give your answer with the correct number of significant figures.106.Determine the number of picoseconds in 2.0 hours.107. Classify each property as intensive or extensive.volumeboiling pointtemperatureelectrical conductivityenergy108.At what temperatures are the readings on the Fahrenheit and Celsius thermometers the same?109.Suppose you design a new thermometer called the X thermometer. On the X scale the boiling point of water is 130 °X, and the freezing point of water is 10 °X. At what temperature are the readings on the Fahrenheit and X thermometers the same?110.On a new Jekyll temperature scale, water freezes at 17 °J and boils at 97 °J. On another new temperature scale, the Hyde scale, water freezes at 0 °H and boils at 120 °H. If methyl alcohol boils at 84 °H, what is its boiling point on the Jekyll scale?111.Force is defined as mass times acceleration. Starting with SI base units, derive a unit for force. Using SI prefixes, suggest a convenient unit for the force resulting from a collision with a 10-ton trailer truck moving at 55 mi per hour and for the force resulting from the collision of a molecule of mass around?10???20??kg?moving almost at the speed of light?(3?×?10?8??m/s?)?with the wall of its container. (Assume a 1-second deceleration time for both collisions.)112.A temperature measurement of 25 °C has three significant figures, while a temperature measurement of –196 °C has only two significant figures. Explain.113.Do each calculation without your calculator and give the answers to the correct number of significant figures.1.76?×?10?–?3?/?8.0?×?10?21.87?×?10?–?2?+?2?×?10?–?4?–?3.0?×?10?–?3[?(?1.36?×?10?5?)?(?0.000322?)?/?0.082?]?(?129.2?)114.The value of the euro was recently $1.15 U.S., and the price of 1 liter of gasoline in France is 1.42 euro. What is the price of 1 gallon of gasoline in U.S. dollars in France?115.A thief uses a can of sand to replace a solid gold cylinder that sits on a weight-sensitive, alarmed pedestal. The can of sand and the gold cylinder have exactly the same dimensions (?length?=?22?and?radius?=?3.8??cm?).Calculate the mass of each cylinder (ignore the mass of the can itself).?(?density?of?gold?=?19.3??g/cm?3?,?density??of?sand?=?3.00???g?/?cm?3?)Does the thief set off the alarm? Explain.116.The proton has a radius of approximately?1.0?×?10???13??cm?and a mass of?1.7?×?10???24?g. Determine the density of a proton for a sphere?V?=?(?4?/?3?)?π?r?3?.117.The density of titanium is?4.51??g/cm?3?. What is the volume (in cubic inches) of 3.5 lb of titanium?118.The density of iron is?7.86??g/cm?3?. What is its density in pounds per cubic inch?(?lb?/?in3?)??119.A steel cylinder has a length of 2.16 in, a radius of 0.22 in, and a mass of 41 g. What is the density of the steel in?g?/?cm?3??120.A solid aluminum sphere has a mass of 85 g. Use the density of aluminum to find the radius of the sphere in inches.121.A backyard swimming pool holds 185 cubic yards?(?yd?3?)?of water. What is the mass of the water in pounds?122.An iceberg has a volume of?7655??ft?2?. What is the mass of the ice (in kg) composing the iceberg (at 0 °C)?123.The Toyota Prius, a hybrid electric vehicle, has an EPA gas mileage rating of 52 mi/gal in the city. How many kilometers can the Prius travel on 15 L of gasoline?124.The Honda Insight, a hybrid electric vehicle, has an EPA gas mileage rating of 41 mi/gal in the city. How many kilometers can the Insight travel on the amount of gasoline that would fit in a soda can? The volume of a soda can is 355 mL.125.The single proton that forms the nucleus of the hydrogen atom has a radius of approximately?1.0?×?10?–?13??cm?. The hydrogen atom itself has a radius of approximately 52.9 pm. What fraction of the space within the atom is occupied by the nucleus?126.A sample of gaseous neon atoms at atmospheric pressure and 0 °C contains?2.69?×?10?22atoms per liter. The atomic radius of neon is 69 pm. What fraction of the space do the atoms themselves occupy? What does this reveal about the separation between atoms in the gaseous phase?127.The diameter of a hydrogen atom is 212 pm. Find the length in kilometers of a row of?6.02?×?10?23?hydrogen atoms. The diameter of a ping pong ball is 4.0 cm. Find the length in kilometers of a row of?6.02?×?10?23?ping pong balls.128.The world’s record in the 100-m dash is 9.69 s, and in the 100-yd dash it is 9.21 s. Find the speed in mi/hr of the runners who set these records. (Assume three significant figures for 100 m and 100 yd.)129.Table salt contains 39.33 g of sodium per 100 g of salt. The U.S. Food and Drug Administration (FDA) recommends that adults consume less than 2.40 g of sodium per day. A particular snack mix contains 1.25 g of salt per 100 g of the mix. What mass of the snack mix can an adult consume and still be within the FDA limit? (Assume three significant figures for 100 g.)130.Lead metal can be extracted from a mineral called galena, which contains 86.6% lead by mass. A particular ore contains 68.5% galena by mass. If the lead can be extracted with 92.5% efficiency, what mass of ore is required to make a lead sphere with a 5.00-cm radius?131.A length of #8 copper wire?(?radius?=?1.63??mm?)?has a mass of 24.0 kg and a resistance of 2.061 ohm per km (Ω/km). What is the overall resistance of the wire?132.Rolls of aluminum foil are 304 mm wide and 0.016 mm thick. What maximum length of aluminum foil can be made from 1.10 kg of aluminum?133.Liquid nitrogen has a density of 0.808 g/mL and boils at 77 K. Researchers often purchase liquid nitrogen in insulated 175 L tanks. The liquid vaporizes quickly to gaseous nitrogen (which has a density of 1.15 g/L at room temperature and atmospheric pressure) when the liquid is removed from the tank. Suppose that all 175 L of liquid nitrogen in a tank accidentally vaporized in a lab that measured?10.00??m?×?10.00??m?×2.50??m?. What maximum fraction of the air in the room could be displaced by the gaseous nitrogen?134.Mercury is often used in thermometers. The mercury sits in a bulb on the bottom of the thermometer and rises up a thin capillary as the temperature rises. Suppose a mercury thermometer contains 3.380 g of mercury and has a capillary that is 0.200 mm in diameter. How far does the mercury rise in the capillary when the temperature changes from 0.0 °C to 25.0 °C? The density of mercury at these temperatures is?13.596??g/cm?3and?13.534??g/cm?3?, respectively.Challenge Problems135.A force of?2.31?×?10?4??N?is applied to a diver’s face mask that has an area of?125??cm?2?. Find the pressure in atm on the face mask.136.The SI unit of force is the newton, derived from the base units by using the definition of force,?F?=?ma?. The dyne is a non-SI unit of force in which mass is measured in grams and time is measured in seconds. The relationship between the two units is?1??dyne?=?10–?5??N?. Find the unit of length used to define the dyne.137.Kinetic energy can be defined as?1?2?m?v?2?or as?3?2?P?V?. Show that the derived SI units of each of these terms are those of energy. (Pressure is force/area and force is mass × acceleration.)138.In 1999, scientists discovered a new class of black holes with masses 100 to 10,000 times the mass of our sun that occupy less space than our moon. Suppose that one of these black holes has a mass of?1?×?10?3?suns and a radius equal to one-half the radius of our moon. What is the density of the black hole in?g/cm?3?? The radius of our sun is?7.0?×?105??km?and it has an average density of?1.4?×?10?3??kg/m?3?. The diameter of the moon is?2.16?×?10?3??mi?.139.Suppose that polluted air has carbon monoxide (CO) levels of 15.0 ppm. An average human inhales about 0.50 L of air per breath and takes about 20 breaths per minute. How many milligrams of carbon monoxide does the average person inhale in an 8-hour period at this level of carbon monoxide pollution? Assume that the carbon monoxide has a density of 1.2 g/L. (Hint: 15.0 ppm CO means 15.0 L CO per?10?6?L air.)140.Nanotechnology, the field of building ultrasmall structures one atom at a time, has progressed in recent years. One potential application of nanotechnology is the construction of artificial cells. The simplest cells would probably mimic red blood cells, the body’s oxygen transporters. Nanocontainers, perhaps constructed of carbon, could be pumped full of oxygen and injected into a person’s bloodstream. If the person needed additional oxygen—due to a heart attack perhaps, or for the purpose of space travel—these containers could slowly release oxygen into the blood, allowing tissues that would otherwise die to remain alive. Suppose that the nanocontainers were cubic and had an edge length of 25 nm.What is the volume of one nanocontainer? (Ignore the thickness of the nanocontainer’s wall.)Suppose that each nanocontainer could contain pure oxygen pressurized to a density of 85 g/L. How many grams of oxygen could each nanocontainer contain?Air typically contains about 0.28 g of oxygen per liter. An average human inhales about 0.50 L of air per breath and takes about 20 breaths per minute. How many grams of oxygen does a human inhale per hour? (Assume two significant figures.)What is the minimum number of nanocontainers that a person would need in his or her bloodstream to provide 1 hour’s worth of oxygen?What is the minimum volume occupied by the number of nanocontainers calculated in part d? Is such a volume feasible, given that total blood volume in an adult is about 5 L?141.Approximate the percent increase in waist size that occurs when a 155-lb person gains 40.0 lb of fat. Assume that the volume of the person can be modeled by a cylinder that is 4.0 ft tall. The average density of a human is about?1.0??g/cm?3?, and the density of fat is?0.918??g/cm?3?.142.A box contains a mixture of small copper spheres and small lead spheres. The total volume of both metals is measured by the displacement of water to be?427??cm?3?,?and the total mass is 4.36 kg. What percentage of the spheres are copper?Conceptual Problems143.A volatile liquid (one that easily evaporates) is put into a jar, and the jar is then sealed. Does the mass of the sealed jar and its contents change upon the vaporization of the liquid?144.The diagram shown first represents solid carbon dioxide, also known as dry ice. Which of the other diagrams best represents the dry ice after it has sublimed into a gas?145.A cube has an edge length of 7 cm. If it is divided into 1-cm cubes, how many 1-cm cubes are there?146.Substance A has density of?1.7??g/cm?3?. Substance B has a density of?1.7??kg/m?3?. Without doing any calculations, determine which substance is more dense.147.For each box, examine the blocks attached to the balances. Based on their positions and sizes, determine which block is more dense (the dark block or the lighter-colored block), or if the relative densities cannot be determined. (Think carefully about the information being shown.)148.Let a triangle represent atoms of element A and a circle represent atoms of element B.Draw an atomic level view of a homogeneous mixture of elements A and B.Draw an atomic view of the compound AB in a liquid state (molecules close together).Draw an atomic view of the compound AB after it has undergone a physical change (such as evaporation).Draw an atomic view of the compound after it has undergone a chemical change (such as decomposition of AB into A and B).149.Identify each statement as being most like an observation, a law, or a theory.All coastal areas experience two high tides and two low tides each day.The tides in Earth’s oceans are caused mainly by the gravitational attraction of the moon.Yesterday, high tide in San Francisco Bay occurred at 2:43?a.m. and 3:07?p.m.Tides are higher at the full moon and new moon than at other times of the month. ................
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